Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.

Making Pathways

Age 7 to 11 Challenge Level:

We have twelve paving slabs of each different colour.
There are three sizes of slabs for each particular colour which are all the same width.

The blue has four of one unit length, four of nine unit length and four of twenty-four unit length.
The green has four of one unit length, four of seven unit length and four of twenty-five unit length.
The red has four of one unit length, four of five unit length and four of twenty-nine unit length.
The lengths cannot be broken into smaller pieces.

Challenge 1

If we were thinking of making a path of length 18 in each colour then we might have:

blue 9 + 9 green 7+7+1+1+1+1 is counted the same as red 5+5+5+1+1+1 is counted the same as

For this challenge you cannot break the paving slabs up into smaller pieces.

Can you make three paths of 22, one in each of the three colours?
Now try three paths of 40, one in each of the three colours.
Lastly try 64, one in each of the three colours.

Challenge 2

How many different ways can you make 75? You cannot mix the colours that are in one path.

Challenge 3

Wouldn't it be good to make eight consecutive lengths of paths that can be made out the blue, green and red - but each separately?

It could look something like this, for the consecutive lengths 59, 60, 61, 62, 63, 64, 65 and 66.
But this is not a solution as it cannot be made without breaking some up into smaller pieces which is not allowed:

Your challenge is to make eight consecutive lengths of path that can be made of each colour separately.

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NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to
embed rich mathematical tasks into everyday classroom practice.